J-PARTITIONS

In this paper, the concept of a J-partition is introduced as a general ization of that of a classical partition. The approach is based on the observation that for any two members of a classical semi-partition, t he nonemptiness of their intersection implies their equality. This obs ervation is generalized to J-semi-partitions using degrees of compatib ility and equality based on a t-norm J and its biresidual operator E-J . By imposing an additional covering condition, the concept of a J-par tition is obtained. An interesting numerical characterization of J-par titions is proved, leading to a desired one-to-one correspondence betw een J-partitions and J-equivalences. Moreover, the refinement of J-par titions is discussed. In particular, it is shown that the J-refinemen t of any two J-partitions of a given universe is again a J-partition o f that universe if and only if the t-norm J dominates the t-norm J. ( C) 1998 Elsevier Science B.V. All rights reserved.